In a large skillet over medium heat, combine broth, evaporated milk and flour. Whisk until mixed and smooth. Continue whisking just until the mixture begins to bubble and the raw flour taste is gone, about 4 min. Add the gizzards, celery, onion, garlic, eggs and ½ tsp pepper and mix thoroughly.
Bring the mixture back to just a simmer, then turn the heat to low and let simmer 5 min, stirring occasionally. Taste for seasoning and adjust as needed.
Set aside off the heat, covered until time to serve.
